Mr Bolsonaro has been staying in Florida since 30 December.
The former president plans to stay in the US while immigration officials process the visa.
He is under investigation in Brazil after rioters stormed key government buildings early this month.
Mr Bolsonaro has voiced “regret” for the unrest, but denies he caused it.
The former president has “devoted 34 years of his life to public service” and would “like to take some time off”, his lawyer, Felipe Alexandre told the BBC in a statement.
Mr Bolsonaro initially travelled to the US on an A-1 visa for diplomats and heads of state, which expires after 30 days. He came to the US ahead of his leftist successor Luiz Inácio Lula da Silva’s 1 January inauguration.
The former president hopes to “clear his head and enjoy being a tourist in the United States for a few months before deciding what his next step will be”, said Mr Alexandre, who works for AG Immigration, an immigration law firm.
US immigration officials received Mr Bolsonaro’s request for a B1/B2 tourism visa last Friday, he said.
On 8 January, thousands of the former president’s supporters attacked federal buildings in Brasília following his defeat in the 2022 general election.
Mr Bolsonaro has faced criticism for the riots where protestors, spurred by unsubstantiated claims of election fraud, broke past security and invaded Brazil’s presidential palace, Congress and Supreme Court.
The former right-wing leader – who has been nicknamed the “Donald Trump of the Tropics” because of his close ties to the former US president – has been staying at the Florida home of former mixed martial arts fighter José Aldo.
His supporters have flocked to the house in the gated community in Kissimmee, Florida, a state where a fifth of Brazilians living in the US reside.
Democratic lawmakers in Washington DC have taken issue with Mr Bolsonaro’s stay in the US. In a letter sent earlier this month, dozens asked President Joe Biden to “revoke” any diplomatic visa Mr Bolsonaro might hold.
“The United States must not provide shelter for him, or any authoritarian who has inspired such violence against democratic institutions,” they wrote.
Mr Alexandre told the Financial Times on Monday that Mr Bolsonaro “bears no responsibility” for the riots.
Source : BBC